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The localized deformation patterns developed during in-plane compression and folding of paperboard have been studied in this work. X-ray post-mortem images reveal that cellulose fibres have been reoriented along localized bands in both the compression and folding tests. In folding, the paperboard typically fails on the side where the compressive stresses exists and wrinkles are formed. The in-plane compression test is however difficult to perform because of the slender geometry of the paperboard. A common technique to determine the compression strength is to use the so-called short-span compression test (SCT). In the SCT, a paperboard with a free length of 0.7 mm is compressed. Another technique to measure the compression strength is the long edge test where the motion of the paperboard is constrained on the top and bottom to prevent buckling. A continuum model that previously has been proposed by the authors is further developed and utilized to predict the occurrence of the localized bands. It is shown that the in-plane strength in compression for paperboard can be correlated to the mechanical behaviour in folding. By tuning the in-plane yield parameters to the SCT response, it is shown that the global response in folding can be predicted. The simulations are able to predict the formation of wrinkles, and the deformation field is in agreement with the measured deformation pattern. The model predicts an unstable material response associated with localized deformation into bands in both the SCT and folding. the machine direction (MD), and the transverse direction to MD is known as the cross direction (CD). The failure stress in ZD is typically two orders of magnitude smaller than the failure stress in MD, while the failure stress in CD is about two to three times lower than MD. To obtain a low weight, paperboard is commonly produced as a sandwiched structure, with stronger mechanical properties in the outer-plies (top and bottom) and weaker properties in the middle. Measurements and simulations have been performed for a single-ply board in this work.Good foldability implies minimum spring back and absence of cracks along fold lines, cf. Cavlin. 1 Because of the bending state present during folding, in-plane compression strength has been attributed for being the dominant factor affecting the foldability of paperboard. The SCT value multiplied with the thickness is shown to be correlated to the maximum bending moment by, for example, Edholm. 4 However, later investigations have confirmed that the out-of-plane shear is an important mechanism to consider during converting procedures, cf. Nygårds et al., 5 Beex and Peerlings, 6 and Borgqvist et al. 7 The in-plane compression strength is difficult to measure because of that structural instabilities (buckling) easily are triggered as a result of the slender geometry of the paperboard. To overcome the difficulties associated with the structural stability in compression tests, short-span length can be used to prevent the buckling. An alternative experimental method is ba...

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The numerical simulation of paperboard creasing and folding processes is of increasing importance for the design and production of safe and reliable packaging systems. The extreme material anisotropy and the complexity of these processes require however simulation capabilities which are seldom available in commercial codes. Several approaches have been proposed in the literature over the years, in most cases making use of non‐linear material models developed ad hoc for this purpose. These models, some of which are very effective and accurate, are not in general available in commercial codes and are often based on the definition of a large number of parameters. In this paper, the possibility to obtain acceptable, first‐hand simulation results using only features already available in a commercial code is investigated. An advanced continuum constitutive model, recently presented in the literature, has been used as a reference for tuning the model and for assessing its accuracy. It is shown how standard features, usually available in state‐of‐the‐art commercial codes, can be employed to deal with the extreme material anisotropy, obtaining qualitatively good results in both the creasing and folding phases. The used standard model accounts for the extremely high anisotropy by means of embedded shell elements, playing the role of reinforcements in the fibre direction. The matrix is assumed to be isotropic and elastoplastic, with properties determined based on the behaviour in the thickness direction. The adopted plasticity model is a modified Drucker–Prager model with a cutoff on the tensile pressure side, available in the used commercial code. The procedure adopted for the identification of the small number of required material parameters is also discussed. Copyright © 2017 John Wiley & Sons, Ltd.

To allow for large‐scale forming applications, such as converting paperboard into package containers, efficient and reliable numerical tools are needed. In finite element simulations of thin structures, elements including structural features are required to reduce the computational cost. Solid‐shell elements based on reduced integration with hourglass stabilization is an attractive choice. One advantage of this choice is the natural inclusion of the thickness, not present in standard degenerated shells, which is especially important for many problems involving contact. Furthermore, no restrictions are imposed on the constitutive models since the solid‐shell element does not require the plane stress condition to be enforced. In this work, a recently proposed efficient solid‐shell element is implemented together with a state‐of‐the‐art continuum model for paperboard. This approach is validated by comparing the obtained numerical results with experimental results for paperboard as well as with those found by using 3D continuum elements. To show the potential of this approach, a large‐scale forming simulation of paperboard is used as a proof of concept.